Let q > 1. Initiated by P. Erdos et al. in [4], several authors studied the numbers l(m)(q) = inf{y: y is an element of Lambda(m), y not equal 0}, m = 1, 2,..., where Lambda(m) denotes the set of all finite sums of the form y = epsilon(0) + epsilon(1) q + epsilon(2)q(2) + ... + epsilon(n)q(n) with integer coefficients -m less than or equal to epsilon(i) less than or equal to m. It is known ([1], [4], [6]) that q is a Pisot number if and only if l(m)(q) > 0 for all m. The value of l(1)(q) was determined for many particular Pisot numbers. but the general case remains widely open. In this paper we determine the value of l(m)(q) in other cases. (C) 2000 Academic Press.

An approximation property of Pisot numbers / Vilmos, Komornik; Loreti, Paola; Marco, Pedicini. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 80:2(2000), pp. 218-237. [10.1006/jnth.1999.2456]

An approximation property of Pisot numbers

LORETI, Paola;
2000

Abstract

Let q > 1. Initiated by P. Erdos et al. in [4], several authors studied the numbers l(m)(q) = inf{y: y is an element of Lambda(m), y not equal 0}, m = 1, 2,..., where Lambda(m) denotes the set of all finite sums of the form y = epsilon(0) + epsilon(1) q + epsilon(2)q(2) + ... + epsilon(n)q(n) with integer coefficients -m less than or equal to epsilon(i) less than or equal to m. It is known ([1], [4], [6]) that q is a Pisot number if and only if l(m)(q) > 0 for all m. The value of l(1)(q) was determined for many particular Pisot numbers. but the general case remains widely open. In this paper we determine the value of l(m)(q) in other cases. (C) 2000 Academic Press.
2000
continuous fractions; diophantine approximation; golden number; pisot numbers
01 Pubblicazione su rivista::01a Articolo in rivista
An approximation property of Pisot numbers / Vilmos, Komornik; Loreti, Paola; Marco, Pedicini. - In: JOURNAL OF NUMBER THEORY. - ISSN 0022-314X. - 80:2(2000), pp. 218-237. [10.1006/jnth.1999.2456]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/466393
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